### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 048, 35 pages      arXiv:1407.4741      https://doi.org/10.3842/SIGMA.2015.048

### General Boundary Formulation for $n$-Dimensional Classical Abelian Theory with Corners

Homero G. Díaz-Marín ab
a) Escuela Nacional de Ingenierí a y Ciencias, Instituto Tecnológico y de Estudios Superiores de Monterrey, C.P. 58350 Morelia, México
b) Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, C.P. 58190 Morelia, México

Received October 30, 2014, in final form June 04, 2015; Published online June 24, 2015

Abstract
We propose a general reduction procedure for classical field theories provided with abelian gauge symmetries in a Lagrangian setting. These ideas come from an axiomatic presentation of the general boundary formulation (GBF) of field theories, mostly inspired by topological quantum field theories (TQFT). We construct abelian Yang-Mills theories using this framework. We treat the case for space-time manifolds with smooth boundary components as well as the case of manifolds with corners. This treatment is the GBF analogue of extended TQFTs. The aim for developing this classical formalism is to accomplish, in a future work, geometric quantization at least for the abelian case.

Key words: gauge fields; action; manifolds with corners.

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